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Friday, 3 August 2018

DISCHARGE OVER A RECTANGULAR NOTCH AND WEIR

We were discussing the various types of notches and weirs i.e. classifications of notches and weirs and also the difference between Notches and Weirs in the subject of fluid mechanics in our recent posts. 

Now we will go ahead to find out the discharge over a rectangular notch or weir, in the subject of fluid mechanics, with the help of this post. 

We must note it here that the expression of the discharge over a rectangular notch or over a weir will be same. 

Now, let us consider that we have channel carrying water and let us think a rectangular notch or weir with this channel as displayed here in following figure. 

We have following data from above figure and these data are as mentioned here. 
H = Head of water over the crest 
L = Length of the rectangular notch or weir 

Let us consider one elementary horizontal strip of water of thickness dh and length L as displayed in above figure. 
dh = Thickness of elementary horizontal strip of water flowing over the rectangular notch or weir 
h = Depth of elementary horizontal strip of water flowing over the rectangular notch or weir 
Cd = Co-efficient of discharge 

Area of elementary horizontal strip of water = L x dh 

We will determine the value of discharge dQ through the elementary horizontal strip of water. After securing the expression for discharge through the elementary horizontal strip, we will integrate the expression between the limit 0 to H and we will have the expression for the discharge over a rectangular notch or weir. 

Now we will go ahead to start a new topic in the subject of fluid mechanics i.e. Discharge over triangular notch or weir with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference:
Fluid mechanics, By R. K. Bansal
Image Courtesy: Google 

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